Averaging percentages is only straightforward when every percentage is based on the same number of people, items or trials. If one class has 120 pupils and another 20, their pass rates should not count equally – a weighted average gives the true overall percentage. This calculator shows both so you can see how much the group sizes matter.
How to use the Average Percentage Calculator
- Number of percentages
- Percent #1
- Sample size #1 (optional)
- Percent #2
- Sample size #2 (optional)
- Percent #3
- Sample size #3 (optional)
- Percent #4
- Sample size #4 (optional)
- Percent #5
- Sample size #5 (optional)
- Percent #6
- Sample size #6 (optional)
- Percent #7
- Sample size #7 (optional)
- Percent #8
- Sample size #8 (optional)
- Percent #9
- Sample size #9 (optional)
- Percent #10
- Sample size #10 (optional)
Results update as you type, and everything is calculated in your browser.
How it works
The simple average adds the percentages and divides by how many there are. The weighted average multiplies each percentage by its sample size, adds those products and divides by the total sample size. With equal sample sizes, the two results are identical.
Inputs explained
| Field | What to enter |
|---|---|
| Number of percentages | Choose one: 2, 3, 4, 5 … |
| Percent #1 | In % |
| Sample size #1 (optional) | A number |
| Percent #2 | In % |
| Sample size #2 (optional) | A number |
| Percent #3 | In % |
| Sample size #3 (optional) | A number |
| Percent #4 | In % |
| Sample size #4 (optional) | A number |
| Percent #5 | In % |
| Sample size #5 (optional) | A number |
| Percent #6 | In % |
| Sample size #6 (optional) | A number |
| Percent #7 | In % |
| Sample size #7 (optional) | A number |
| Percent #8 | In % |
| Sample size #8 (optional) | A number |
| Percent #9 | In % |
| Sample size #9 (optional) | A number |
| Percent #10 | In % |
| Sample size #10 (optional) | A number |
Example values
How the main result changes when Percent #1 changes and everything else stays at the example values above:
| Percent #1 (%) | Simple average (%) |
|---|---|
| 31 | 58.5 |
| 46.5 | 62.375 |
| 62 | 66.25 |
| 77.5 | 70.125 |
| 93 | 74 |
| 124 | 81.75 |
Formula
Simple average = (p₁ + p₂ + … + pₙ) ÷ n
Weighted average = (p₁·n₁ + p₂·n₂ + … + pₖ·nₖ) ÷ (n₁ + n₂ + … + nₖ)
Worked example
Inputs — Number of percentages: 4; Percent #1: 62 %; Sample size #1 (optional): 120; Percent #2: 75 %; Sample size #2 (optional): 80; Percent #3: 58 %; Sample size #3 (optional): 200; Percent #4: 70 %; Sample size #4 (optional): 50.
Results — Simple average = 66.25 %; Weighted average (by sample size) = 63.4222 %; Total sample size = 450; Total "successes" (pooled count) = 285.4.
Key terms
- Weighted average
- An average in which each value counts in proportion to a weight, here the sample size.
- Pooled percentage
- The percentage of successes in all groups combined.
Frequently asked questions
Can I just average percentages?
Only if every percentage comes from a group of the same size. Otherwise use the weighted average, which counts each group in proportion to its size.
Why is the weighted average different?
Larger groups pull the average towards their own percentage. The weighted figure equals the percentage you would get by pooling all the raw counts.
What if I do not know the sample sizes?
Leave every sample size at the same value (for example 1); the weighted average then equals the simple average.
Can percentages above 100% be averaged?
Yes – growth rates or percentages of a target can exceed 100%, and the same formulas apply.